Refinement and Pattern Formation in Neural Circuits by the Interaction of Traveling Waves with Spike-Timing Dependent Plasticity

Traveling waves in the developing brain are a prominent source of highly correlated spiking activity that may instruct the refinement of neural circuits. A candidate mechanism for mediating such refinement is spike-timing dependent plasticity (STDP), which translates correlated activity patterns into changes in synaptic strength. To assess the potential of these phenomena to build useful structure in developing neural circuits, we examined the interaction of wave activity with STDP rules in simple, biologically plausible models of spiking neurons. We derive an expression for the synaptic strength dynamics showing that, by mapping the time dependence of STDP into spatial interactions, traveling waves can build periodic synaptic connectivity patterns into feedforward circuits with a broad class of experimentally observed STDP rules. The spatial scale of the connectivity patterns increases with wave speed and STDP time constants. We verify these results with simulations and demonstrate their robustness to likely sources of noise. We show how this pattern formation ability, which is analogous to solutions of reaction-diffusion systems that have been widely applied to biological pattern formation, can be harnessed to instruct the refinement of postsynaptic receptive fields. Our results hold for rich, complex wave patterns in two dimensions and over several orders of magnitude in wave speeds and STDP time constants, and they provide predictions that can be tested under existing experimental paradigms. Our model generalizes across brain areas and STDP rules, allowing broad application to the ubiquitous occurrence of traveling waves and to wave-like activity patterns induced by moving stimuli.     

Traveling waves and pulses in a one-dimensional network of excitable integrate-and-fire neurons

 We study the existence and stability of traveling waves and pulses in a one-dimensional network of integrate-and-fire neurons with synaptic coupling. This provides a simple model of excitable neural tissue. We first derive a self-consistency condition for the existence of traveling waves, which generates a dispersion relation between velocity and wavelength. We use this to investigate how wave-propagation depends on various parameters that characterize neuronal interactions such as synaptic and axonal delays, and the passive membrane properties of dendritic cables. We also establish that excitable networks support the propagation of solitary pulses in the long-wavelength limit. We then derive a general condition for the (local) asymptotic stability of traveling waves in terms of the characteristic equation of the linearized firing time map, which takes the form of an integro-difference equation of infinite order. We use this to analyze the stability of solitary pulses in the long-wavelength limit. Solitary wave solutions are shown to come in pairs with the faster (slower) solution stable (unstable) in the case of zero axonal delays; for non-zero delays and fast synapses the stable wave can itself destabilize via a Hopf bifurcation. Received: 27 October 1998     

Presynaptic plasticity and associative learning are impaired in a Drosophila presenilin null mutant

Alzheimer's disease is a neurodegenerative disorder characterized by progressive memory and cognitive decline that is associated with changes in synaptic plasticity and neuronal cell loss. Recent evidence suggests that some of these defects may be due to a loss of normal presenilin activity. Here, we have examined the effect of loss of Drosophila presenilin (psn) function on synaptic plasticity and learning. Basal transmitter release was elevated in psn mutants while both paired pulse synaptic plasticity and post-tetanic potentiation were impaired. These defects in synaptic strength and plasticity were not due to developmental defects in NMJ morphology. We also found that psn null terminals take up significantly less FM 4-64 than control terminals when loaded with high frequency stimulation, suggesting a defect in synaptic vesicle availability or mobilization. To determine whether these reductions in synaptic plasticity had any impact on learning, we tested the larvae for defects in associative learning. Using both olfactory and visual learning assays, we found that associative learning is impaired in psn mutants compared with controls. Both the learning and synaptic defects could be rescued by expression of a full length psn transgene suggesting the defects are specifically due to a loss of psn function. Taken together, these results provide the first evidence of learning and synaptic defects in a Drosophila psn mutant and strongly suggest a presynaptic role for presenilin in normal neuronal function.     

Somato-dendritic Synaptic Plasticity and Error-backpropagation in Active Dendrites

In the last decade dendrites of cortical neurons have been shown to nonlinearly combine synaptic inputs by evoking local dendritic spikes. It has been suggested that these nonlinearities raise the computational power of a single neuron, making it comparable to a 2-layer network of point neurons. But how these nonlinearities can be incorporated into the synaptic plasticity to optimally support learning remains unclear. We present a theoretically derived synaptic plasticity rule for supervised and reinforcement learning that depends on the timing of the presynaptic, the dendritic and the postsynaptic spikes. For supervised learning, the rule can be seen as a biological version of the classical error-backpropagation algorithm applied to the dendritic case. When modulated by a delayed reward signal, the same plasticity is shown to maximize the expected reward in reinforcement learning for various coding scenarios. Our framework makes specific experimental predictions and highlights the unique advantage of active dendrites for implementing powerful synaptic plasticity rules that have access to downstream information via backpropagation of action potentials.     

SRC3 acetylates calmodulin in the mouse brain to regulate synaptic plasticity and fear learning

Protein acetylation is a reversible posttranslational modification, which is regulated by lysine acetyltransferase (KAT) and lysine deacetyltransferase (KDAC). Although protein acetylation has been shown to regulate synaptic plasticity, this was mainly for histone protein acetylation. The function and regulation of nonhistone protein acetylation in synaptic plasticity and learning remain largely unknown. Calmodulin (CaM), a ubiquitous Ca²⁺ sensor, plays critical roles in synaptic plasticity such as long-term potentiation (LTP). During LTP induction, activation of NMDA receptor triggers Ca²⁺ influx, and the Ca²⁺ binds with CaM and activates calcium/calmodulin-dependent protein kinase IIα (CaMKIIα). In our previous study, we demonstrated that acetylation of CaM was important for synaptic plasticity and fear learning in mice. However, the KAT responsible for CaM acetylation is currently unknown. Here, following an HEK293 cell-based screen of candidate KATs, steroid receptor coactivator 3 (SRC3) is identified as the most active KAT for CaM. We further demonstrate that SRC3 interacts with and acetylates CaM in a Ca²⁺ and NMDA receptor-dependent manner. We also show that pharmacological inhibition or genetic downregulation of SRC3 impairs CaM acetylation, synaptic plasticity, and contextual fear learning in mice. Moreover, the effects of SRC3 inhibition on synaptic plasticity and fear learning could be rescued by 3KQ-CaM, a mutant form of CaM, which mimics acetylation. Together, these observations demonstrate that SRC3 acetylates CaM and regulates synaptic plasticity and learning in mice.     

A Calcium-Dependent Plasticity Rule for HCN Channels Maintains Activity Homeostasis and Stable Synaptic Learning

Theoretical and computational frameworks for synaptic plasticity and learning have a long and cherished history, with few parallels within the well-established literature for plasticity of voltage-gated ion channels. In this study, we derive rules for plasticity in the hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, and assess the synergy between synaptic and HCN channel plasticity in establishing stability during synaptic learning. To do this, we employ a conductance-based model for the hippocampal pyramidal neuron, and incorporate synaptic plasticity through the well-established Bienenstock-Cooper-Munro (BCM)-like rule for synaptic plasticity, wherein the direction and strength of the plasticity is dependent on the concentration of calcium influx. Under this framework, we derive a rule for HCN channel plasticity to establish homeostasis in synaptically-driven firing rate, and incorporate such plasticity into our model. In demonstrating that this rule for HCN channel plasticity helps maintain firing rate homeostasis after bidirectional synaptic plasticity, we observe a linear relationship between synaptic plasticity and HCN channel plasticity for maintaining firing rate homeostasis. Motivated by this linear relationship, we derive a calcium-dependent rule for HCN-channel plasticity, and demonstrate that firing rate homeostasis is maintained in the face of synaptic plasticity when moderate and high levels of cytosolic calcium influx induced depression and potentiation of the HCN-channel conductance, respectively. Additionally, we show that such synergy between synaptic and HCN-channel plasticity enhances the stability of synaptic learning through metaplasticity in the BCM-like synaptic plasticity profile. Finally, we demonstrate that the synergistic interaction between synaptic and HCN-channel plasticity preserves robustness of information transfer across the neuron under a rate-coding schema. Our results establish specific physiological roles for experimentally observed plasticity in HCN channels accompanying synaptic plasticity in hippocampal neurons, and uncover potential links between HCN-channel plasticity and calcium influx, dynamic gain control and stable synaptic learning.     

Pre- and postsynaptically expressed spike-timing-dependent plasticity contribute differentially to neuronal learning

A plethora of experimental studies have shown that long-term synaptic plasticity can be expressed pre- or postsynaptically depending on a range of factors such as developmental stage, synapse type, and activity patterns. The functional consequences of this diversity are not clear, although it is understood that whereas postsynaptic expression of plasticity predominantly affects synaptic response amplitude, presynaptic expression alters both synaptic response amplitude and short-term dynamics. In most models of neuronal learning, long-term synaptic plasticity is implemented as changes in connective weights. The consideration of long-term plasticity as a fixed change in amplitude corresponds more closely to post- than to presynaptic expression, which means theoretical outcomes based on this choice of implementation may have a postsynaptic bias. To explore the functional implications of the diversity of expression of long-term synaptic plasticity, we adapted a model of long-term plasticity, more specifically spike-timing-dependent plasticity (STDP), such that it was expressed either independently pre- or postsynaptically, or in a mixture of both ways. We compared pair-based standard STDP models and a biologically tuned triplet STDP model, and investigated the outcomes in a minimal setting, using two different learning schemes: in the first, inputs were triggered at different latencies, and in the second a subset of inputs were temporally correlated. We found that presynaptic changes adjusted the speed of learning, while postsynaptic expression was more efficient at regulating spike timing and frequency. When combining both expression loci, postsynaptic changes amplified the response range, while presynaptic plasticity allowed control over postsynaptic firing rates, potentially providing a form of activity homeostasis. Our findings highlight how the seemingly innocuous choice of implementing synaptic plasticity by single weight modification may unwittingly introduce a postsynaptic bias in modelling outcomes. We conclude that pre- and postsynaptically expressed plasticity are not interchangeable, but enable complimentary functions.     

Soft-bound Synaptic Plasticity Increases Storage Capacity

Accurate models of synaptic plasticity are essential to understand the adaptive properties of the nervous system and for realistic models of learning and memory. Experiments have shown that synaptic plasticity depends not only on pre- and post-synaptic activity patterns, but also on the strength of the connection itself. Namely, weaker synapses are more easily strengthened than already strong ones. This so called soft-bound plasticity automatically constrains the synaptic strengths. It is known that this has important consequences for the dynamics of plasticity and the synaptic weight distribution, but its impact on information storage is unknown. In this modeling study we introduce an information theoretic framework to analyse memory storage in an online learning setting. We show that soft-bound plasticity increases a variety of performance criteria by about 18% over hard-bound plasticity, and likely maximizes the storage capacity of synapses.     

Multiple-spike waves in a one-dimensional integrate-and-fire neural network

This paper builds on the past study of single-spike waves in one-dimensional integrate-and-fire networks to provide a framework for the study of waves with arbitrary (finite or countably infinite) collections of spike times. Based on this framework, we prove an existence theorem for single-spike traveling waves, and we combine analysis and numerics to study two-spike traveling waves, periodic traveling waves, and general infinite spike trains. For a fixed wave speed, finite-spike waves, periodic waves, and other infinite-spike waves may all occur, and we discuss the relationships among them. We also relate the waves considered analytically to waves generated in numerical simulations by the transient application of localized excitation.Key words or phrases:Traveling waves, Integrate-and-fire network, Excitatory synaptic coupling     

Phenomenological models of synaptic plasticity based on spike timing

Synaptic plasticity is considered to be the biological substrate of learning and memory. In this document we review phenomenological models of short-term and long-term synaptic plasticity, in particular spike-timing dependent plasticity (STDP). The aim of the document is to provide a framework for classifying and evaluating different models of plasticity. We focus on phenomenological synaptic models that are compatible with integrate-and-fire type neuron models where each neuron is described by a small number of variables. This implies that synaptic update rules for short-term or long-term plasticity can only depend on spike timing and, potentially, on membrane potential, as well as on the value of the synaptic weight, or on low-pass filtered (temporally averaged) versions of the above variables. We examine the ability of the models to account for experimental data and to fulfill expectations derived from theoretical considerations. We further discuss their relations to teacher-based rules (supervised learning) and reward-based rules (reinforcement learning). All models discussed in this paper are suitable for large-scale network simulations.     

Stability of complex spike timing-dependent plasticity in cerebellar learning

Dynamics of spike-timing dependent synaptic plasticity are analyzed for excitatory and inhibitory synapses onto cerebellar Purkinje cells. The purpose of this study is to place theoretical constraints on candidate synaptic learning rules that determine the changes in synaptic efficacy due to pairing complex spikes with presynaptic spikes in parallel fibers and inhibitory interneurons. Constraints are derived for the timing between complex spikes and presynaptic spikes, constraints that result from the stability of the learning dynamics of the learning rule. Potential instabilities in the parallel fiber synaptic learning rule are found to be stabilized by synaptic plasticity at inhibitory synapses if the inhibitory learning rules are stable, and conditions for stability of inhibitory plasticity are given. Combining excitatory with inhibitory plasticity provides a mechanism for minimizing the overall synaptic input. Stable learning rules are shown to be able to sculpt simple-spike patterns by regulating the excitability of neurons in the inferior olive that give rise to climbing fibers.     

Modulation of synaptic plasticity by stress hormone associates with plastic alteration of synaptic NMDA receptor in the adult hippocampus

Stress exerts a profound impact on learning and memory, in part, through the actions of adrenal corticosterone (CORT) on synaptic plasticity, a cellular model of learning and memory. Increasing findings suggest that CORT exerts its impact on synaptic plasticity by altering the functional properties of glutamate receptors, which include changes in the motility and function of α-amino-3-hydroxy-5-methylisoxazole-4-propionic acid subtype of glutamate receptor (AMPAR) that are responsible for the expression of synaptic plasticity. Here we provide evidence that CORT could also regulate synaptic plasticity by modulating the function of synaptic N-methyl-D-aspartate receptors (NMDARs), which mediate the induction of synaptic plasticity. We found that stress level CORT applied to adult rat hippocampal slices potentiated evoked NMDAR-mediated synaptic responses within 30 min. Surprisingly, following this fast-onset change, we observed a slow-onset (>1 hour after termination of CORT exposure) increase in synaptic expression of GluN2A-containing NMDARs. To investigate the consequences of the distinct fast- and slow-onset modulation of NMDARs for synaptic plasticity, we examined the formation of long-term potentiation (LTP) and long-term depression (LTD) within relevant time windows. Paralleling the increased NMDAR function, both LTP and LTD were facilitated during CORT treatment. However, 1-2 hours after CORT treatment when synaptic expression of GluN2A-containing NMDARs is increased, bidirectional plasticity was no longer facilitated. Our findings reveal the remarkable plasticity of NMDARs in the adult hippocampus in response to CORT. CORT-mediated slow-onset increase in GluN2A in hippocampal synapses could be a homeostatic mechanism to normalize synaptic plasticity following fast-onset stress-induced facilitation.     

Learning flexible sensori-motor mappings in a complex network

Given the complex structure of the brain, how can synaptic plasticity explain the learning and forgetting of associations when these are continuously changing? We address this question by studying different reinforcement learning rules in a multilayer network in order to reproduce monkey behavior in a visuomotor association task. Our model can only reproduce the learning performance of the monkey if the synaptic modifications depend on the pre- and postsynaptic activity, and if the intrinsic level of stochasticity is low. This favored learning rule is based on reward modulated Hebbian synaptic plasticity and shows the interesting feature that the learning performance does not substantially degrade when adding layers to the network, even for a complex problem.     

A burst-based "Hebbian" learning rule at retinogeniculate synapses links retinal waves to activity-dependent refinement

Patterned spontaneous activity in the developing retina is necessary to drive synaptic refinement in the lateral geniculate nucleus (LGN). Using perforated patch recordings from neurons in LGN slices during the period of eye segregation, we examine how such burst-based activity can instruct this refinement. Retinogeniculate synapses have a novel learning rule that depends on the latencies between pre- and postsynaptic bursts on the order of one second: coincident bursts produce long-lasting synaptic enhancement, whereas non-overlapping bursts produce mild synaptic weakening. It is consistent with “Hebbian” development thought to exist at this synapse, and we demonstrate computationally that such a rule can robustly use retinal waves to drive eye segregation and retinotopic refinement. Thus, by measuring plasticity induced by natural activity patterns, synaptic learning rules can be linked directly to their larger role in instructing the patterning of neural connectivity.     

A Burst-Based “Hebbian” Learning Rule at Retinogeniculate Synapses Links Retinal Waves to Activity-Dependent Refinement

Patterned spontaneous activity in the developing retina is necessary to drive synaptic refinement in the lateral geniculate nucleus (LGN). Using perforated patch recordings from neurons in LGN slices during the period of eye segregation, we examine how such burst-based activity can instruct this refinement. Retinogeniculate synapses have a novel learning rule that depends on the latencies between pre- and postsynaptic bursts on the order of one second: coincident bursts produce long-lasting synaptic enhancement, whereas non-overlapping bursts produce mild synaptic weakening. It is consistent with “Hebbian” development thought to exist at this synapse, and we demonstrate computationally that such a rule can robustly use retinal waves to drive eye segregation and retinotopic refinement. Thus, by measuring plasticity induced by natural activity patterns, synaptic learning rules can be linked directly to their larger role in instructing the patterning of neural connectivity.     

Formation and Dynamics of Waves in a Cortical Model of Cholinergic Modulation

Acetylcholine (ACh) is a regulator of neural excitability and one of the neurochemical substrates of sleep. Amongst the cellular effects induced by cholinergic modulation are a reduction in spike-frequency adaptation (SFA) and a shift in the phase response curve (PRC). We demonstrate in a biophysical model how changes in neural excitability and network structure interact to create three distinct functional regimes: localized asynchronous, traveling asynchronous, and traveling synchronous. Our results qualitatively match those observed experimentally. Cortical activity during slow wave sleep (SWS) differs from that during REM sleep or waking states. During SWS there are traveling patterns of activity in the cortex; in other states stationary patterns occur. Our model is a network composed of Hodgkin-Huxley type neurons with a M-current regulated by ACh. Regulation of ACh level can account for dynamical changes between functional regimes. Reduction of the magnitude of this current recreates the reduction in SFA the shift from a type 2 to a type 1 PRC observed in the presence of ACh. When SFA is minimal (in waking or REM sleep state, high ACh) patterns of activity are localized and easily pinned by network inhomogeneities. When SFA is present (decreasing ACh), traveling waves of activity naturally arise. A further decrease in ACh leads to a high degree of synchrony within traveling waves. We also show that the level of ACh determines how sensitive network activity is to synaptic heterogeneity. These regimes may have a profound functional significance as stationary patterns may play a role in the proper encoding of external input as memory and traveling waves could lead to synaptic regularization, giving unique insights into the role and significance of ACh in determining patterns of cortical activity and functional differences arising from the patterns.     

Neural fields with fast learning dynamic kernel

We introduce a modified-firing-rate model based on Hebbian-type changing synaptic connections. The existence and stability of solutions such as rest state, bumps, and traveling waves are shown for this type of model. Three types of kernels, namely exponential, Mexican hat, and periodic synaptic connections, are considered. In the former two cases, the existence of a rest state solution is proved and the conditions for their stability are found. Bump solutions are shown for two kinds of synaptic kernels, and their stability is investigated by constructing a corresponding Evans function that holds for a specific range of values of the kernel coefficient strength (KCS). Applying a similar method, we consider exponential synaptic connections, where traveling wave solutions are shown to exist. Simulation and numerical analysis are presented for all these cases to illustrate the resulting solutions and their stability.